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Primitive Operations in Phonology Bridget Samuels Harvard University UMD - May 20, 2009 Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 1 / 29 Introduction My focus : the nature of phonological representations

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SLIDE 1

Primitive Operations in Phonology

Bridget Samuels

Harvard University

UMD - May 20, 2009

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 1 / 29

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Introduction

My focus: the nature of phonological representations &

  • perations, and how phonology is situated with respect to the

linguistic module and cognition more generally. I attempt to provide a phonological companion to, e.g., Hornstein (2009) and Hornstein & Pietroski (To appear) Today’s goal: develop a theory of ‘generalized search and copy,’ uniting the representations of Raimy (1999, et seq.) with the operations of Mailhot & Reiss (2007) and extending this approach to all of (morpho)phonology.

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 2 / 29

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SLIDE 3

Introduction

My focus: the nature of phonological representations &

  • perations, and how phonology is situated with respect to the

linguistic module and cognition more generally. I attempt to provide a phonological companion to, e.g., Hornstein (2009) and Hornstein & Pietroski (To appear) Today’s goal: develop a theory of ‘generalized search and copy,’ uniting the representations of Raimy (1999, et seq.) with the operations of Mailhot & Reiss (2007) and extending this approach to all of (morpho)phonology.

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 2 / 29

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Introduction

Poeppel (2005): “Linguists. . . owe a decomposition (or fractionation) of the particular linguistic domain in question. . . into formal

  • perations that are, ideally, elemental and generic. The types
  • f computations one might entertain, for example, include

concatenation, comparison, or recursion. Generic formal

  • perations at this level of abstraction can form the basis for

more complex linguistic representation and computation.”

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 3 / 29

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Starting point

Reduplication is affixation (Marantz 1982). Both are driven by the need to find a host for a newly-introduced morpheme. Each time a string enters the phonological workspace, before anything else happens, it must be combined with the string which is already present. Raimy (1999, et seq.) establishes a directed graph notation for phonological representations, which are conceived of as strings of segments ordered by precedence relationships. /kæt/ is shorthand for: # → k → æ→ t → %

  • r as ordered pairs:

(#, k), (k, æ), (æ, t), (t, %)

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 4 / 29

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SLIDE 6

Starting point

Reduplication is affixation (Marantz 1982). Both are driven by the need to find a host for a newly-introduced morpheme. Each time a string enters the phonological workspace, before anything else happens, it must be combined with the string which is already present. Raimy (1999, et seq.) establishes a directed graph notation for phonological representations, which are conceived of as strings of segments ordered by precedence relationships. /kæt/ is shorthand for: # → k → æ→ t → %

  • r as ordered pairs:

(#, k), (k, æ), (æ, t), (t, %)

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 4 / 29

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Starting point

Representations must be flat for the S-M system ∴ 3-D or ‘non-asymmetric’ structures (loops) must be repaired # → k → æ→ t → % /kætkæt/ # → p → u → k → % /puhk/ h

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 5 / 29

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Typology

Reduplication Morphology may direct the insertion of a new precedence relationship which creates a ‘backward’ loop in the string Add (t, k): # → k → æ→ t → % = /kætkæt/

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 6 / 29

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Typology

Affixation & Templatic Morphology Morphology may also create a ‘forward’ loop Add (X, Z), (Z, Y): # → X → Y → % = XZY Z # → w → a → n → t → % e → d → %

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 6 / 29

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Typology

Subtractive Morphology ‘Jump links,’ or forward loops which skip one or more lexical segments, cannot be ruled out without additional stipulations (Gagnon & Pich´ e 2007, Gagnon 2008) Add (o, %): # → g → o → l → o → n → %

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 6 / 29

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Typology

Metathesis Halle (2008) adds metathesis to the list of processes which can be described in these terms. Add: (#, B), (A, C), C, A): # → A → B → C → % = BCA

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 6 / 29

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Search & Copy

Problem: loops can’t be just anywhere. Typology established in Samuels (2009), §4.3.1-3: {first, second, stressed, penult, last} element of type {X, C, V, foot}. Solution: use a search algorithm with a limited set of parameters such as that of Mailhot & Reiss (2007)

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 7 / 29

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Search & Copy

Search (Σ, ς, γ, δ)

  • 1. Find all x in Σ subsumed by ς and index them:

ς0, ς1, . . . , ςn

  • 2. For each i ∈ {0, . . . , n}:

(a) Proceed from ςi through Σ in the direction δ until an element subsumed by γ is found (b) Label this element γi

  • 3. Return all pairs of coindexed standards and goals, (ςi, γi)

Copy (Σ, ς, γ, C)

Identify αF on γi and assign αF to ςi if the set of conditions C on γi are satisfied

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 7 / 29

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Harmony via Search & Copy

Wolof [ATR] harmony (M&R 38) a. toxi-lEEn [toxileen] ‘go and smoke’ (imper.) b. tEkki-lEEn [tEkkilEEn] ‘untie’ (imper.) c. seen-uw-OOn [seenuwoon] ‘tried to spot’ d. tEEr-uw-OOn [tEEruwOOn] ‘welcomed’ Search δ = L for γ specified [-high, αATR] Copy [αATR] back to ς.

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 8 / 29

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Morphophonology via Search & Copy

To apply search & copy to morphophonological anchoring: Affixhood means lacking #, %, or both. This means there is a ‘sticky end’ (ς) on the affix which enables it to concatenate with another string. ςi → e → d → % Divorce ς from the beginning point of search (call it β; β = #, %, or γn−1) Copy places γi into a precedence pair: (ςi, e)

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 9 / 29

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Morphophonology via Search & Copy

To apply search & copy to morphophonological anchoring: Affixhood means lacking #, %, or both. This means there is a ‘sticky end’ (ς) on the affix which enables it to concatenate with another string. ςi → e → d → % Divorce ς from the beginning point of search (call it β; β = #, %, or γn−1) Copy places γi into a precedence pair: (ςi, e)

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 9 / 29

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Morphophonology via Search & Copy

To apply search & copy to morphophonological anchoring: Affixhood means lacking #, %, or both. This means there is a ‘sticky end’ (ς) on the affix which enables it to concatenate with another string. ςi → e → d → % Divorce ς from the beginning point of search (call it β; β = #, %, or γn−1) Copy places γi into a precedence pair: (ςi, e)

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 9 / 29

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Suffixation

Σ (string in the active workspace): # → w → a → n → t → % ς (initiator of search): ςi → e → d → % γ (target of search): First X δ (direction of search): L (i.e., beginning at %) Copy γi to ςi. # → w → a → n → t → % e → d → %

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 10 / 29

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Infixation

For infixes, two applications of search, with γi = βj. Budukh durative (Yu 2007:103) a. ˇ coˇ su ˇ co-r-ˇ su ‘to stab (downwards)’ b. saq’a sa-r-q’a ‘to die’ c. saPar sa-r-Par ‘to become dry’ ς (initiator of search): ςi → r → ςj γ (target of search): γi = First V; γj = First X δ (direction of search): R β (beginning point of search): βi = #; βj = γi # → ˇ c → o → ˇ s → u → % r

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 11 / 29

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Subtractive morphology

Tohono O’odham (Zepeda 1983, Gagnon & Pich´ e 2007) Imperfective Perfective a. hi:nk hi:n ‘bark(ed)’ b. ˜ neid ˜ nei ‘see/saw’ c. golon golo ‘rake’ ς (initiator of search): ςi → ςj γ (target of search): γi: Second X; γj: % δ (direction of search): δi: L; δj: R β (beginning point of search): βi: %; βj: γi # → g → o → l → o → n → %

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 12 / 29

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Reduplication

In the case of reduplication, the affix enters with two sticky ends. The second search can begin at #, %, or γi. English shm-reduplication ς (initiator of search): ςi → sh → m → ςj γ (target of search): γi = First X; γj = First V δ (direction of search): δi = L; δj = R β (beginning point of search): βi = %; βj = # # → f → a → → n → c → y → % shm

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 13 / 29

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Reduplication

Kamaiur´ a aspectual reduplication (Yu 2007:111) Singular Plural a.

  • mokon
  • moko-moko-n

‘he swallowed it (frequently)’ b.

  • huka
  • huka-huka

‘he (kept on) laughing’ c. jeumirik jeumiri-miri-k ‘I tie up (repeatedly)’ ς (initiator of search): ςi → ςj γ (target of search): γi = First V; γj = Second C δ (direction of search): δ: L β (beginning point of search): βi = %; βj = γi # → o → m → o → k → o → n → %

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 13 / 29

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Further consequences

Corollary: loop direction is epiphenomenal. ς (initiator of search): ςi → ςj γ (target of search): γi = ´ V; γj = Second V δ (direction of search): R β (beginning point of search): % # → C → V → C → V → C → ´ V → % # → C → ´ V → C → V → C → V → %

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 14 / 29

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From loops to strings

The linearized output (see Fitzpatrick (2006)): Takes the shortest path through the graph (Economy) Realizes as many precedence relations as possible (Completeness) Realizes m-links in preference to lexical links Takes the shortest loops first (Shortest)

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 15 / 29

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From loops to strings

Same results, no constraints: Idsardi & Shorey’s (2007) modified version of Dijkstra’s shortest path algorithm (Dijkstra 1959). To linearize: (#, k), (k, æ), (æ, t), (t, %) Vertices: {#, k, æ, t, %} Initial queue: 1) # → k 2) k → æ 3) æ→ t 4) t → %

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 16 / 29

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Linearizing (#, k), (k, æ), (æ, t), (t, %)

Step 1 (begin at #) Traverse path: # → k Output: # → k New queue: 1) k → æ 2) æ→ t 3) t → % 4) # → k

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 17 / 29

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Linearizing (#, k), (k, æ), (æ, t), (t, %)

Step 2 (begin at /k/) Traverse path: k → æ Output: # → k → æ New queue: 1) æ→ t 2) t → % 3) # → k 4) k → æ

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 17 / 29

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Linearizing (#, k), (k, æ), (æ, t), (t, %)

Step 3 (begin at /æ/) Traverse path: æ→ t Output: # → k → æ→ t New queue: 1) t → % 2) # → k 3) k → æ 4) æ→ t

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 17 / 29

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Linearizing (#, k), (k, æ), (æ, t), (t, %)

The algorithm then reaches %: Step 4 (begin at /t/) Traverse path: t → % Output: # → k → æ→ t → % Algorithm halts. Since each vertex was the starting point for only one path, the order of the statements in the queue did not actually matter; any ordering of statements would have yielded the same output. But this is not the case when there are loops.

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 17 / 29

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Linearizing (t, k), (#, k), (k, æ), (æ, t), (t, %)

If we add (t, k), to the bottom of the queue, nothing changes. But if we add (t, k) above (t, %), everything proceeds as above until Step 4: Step 3 (begin at /æ/) Traverse path: æ→ t # → k → æ→ t New queue: 1) t → k 2) t → % 3) # → k 4) k → æ 5) æ→ t

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 18 / 29

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Linearizing (t, k), (#, k), (k, æ), (æ, t), (t, %)

Step 4 (begin at /t/) Traverse path: t → k # → k → æ→ t → k New queue: 1) t → % 2) # → k 3) k → æ 4) æ→ t 5) t → k

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 18 / 29

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Linearizing (t, k), (#, k), (k, æ), (æ, t), (t, %)

Step 5 (begin at /k/) Traverse path: k → æ # → k → æ→ t → k → æ New queue: 1) t → % 2) # → k 3) æ→ t 4) t → k 5) k → æ

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 18 / 29

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Linearizing (t, k), (#, k), (k, æ), (æ, t), (t, %)

Step 6 (begin at /æ/) Traverse path: æ→ t # → k → æ→ t → k → æ→ t New queue: 1) t → % 2) # → k 3) t → k 4) k → æ 5) æ→ t

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 18 / 29

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Linearizing (t, k), (#, k), (k, æ), (æ, t), (t, %)

Finally, the algorithm hits %: Step 7 (begin at /t/) Traverse path: t → % Output: # → k → æ→ t → k → æ→ t → % Algorithm halts.

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 18 / 29

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More on linearization

If precedence relations established by search and copy are always added to the top of the queue, we get an asymmetric string which realizes m-links in preference to lexical material, and is

  • economical. (No loops in the lexicon: Gagnon (2007), contra

Fitzpatrick (2006)) In Samuels (2009), §4.3.6 I discuss the evidence from Lushootseed for Shortest and propose an alternative. I also discuss over-/under-application and argue linearization applies immediately upon concatenation (cf. Raimy (2000)).

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 19 / 29

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SLIDE 36

More on linearization

If precedence relations established by search and copy are always added to the top of the queue, we get an asymmetric string which realizes m-links in preference to lexical material, and is

  • economical. (No loops in the lexicon: Gagnon (2007), contra

Fitzpatrick (2006)) In Samuels (2009), §4.3.6 I discuss the evidence from Lushootseed for Shortest and propose an alternative. I also discuss over-/under-application and argue linearization applies immediately upon concatenation (cf. Raimy (2000)).

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 19 / 29

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SLIDE 37

More on linearization

If precedence relations established by search and copy are always added to the top of the queue, we get an asymmetric string which realizes m-links in preference to lexical material, and is

  • economical. (No loops in the lexicon: Gagnon (2007), contra

Fitzpatrick (2006)) In Samuels (2009), §4.3.6 I discuss the evidence from Lushootseed for Shortest and propose an alternative. I also discuss over-/under-application and argue linearization applies immediately upon concatenation (cf. Raimy (2000)).

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 19 / 29

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Generalized Search & Copy

As early as SPE, it was recognized that rule application could be seen as a search plus modification procedure (see also Mailhot & Reiss (2007:30)): “To apply a rule, the entire string is first scanned for segments that satisfy the environmental constraints of the

  • rule. After all such segments have been identified in the

string, the changes required by the rule are applied simultaneously.” (Chomsky & Halle 1968:344)

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 20 / 29

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Generalized Search & Copy

Search simplifies rules and preserves important insights from autosegmental phonology while streamlining representations. V → [+F] / C0# stands for an infinite set of simultaneously-applying rules: a. V → [+F] / # b. V → [+F] / C# c. V → [+F] / CC# d. V → [+F] / CCC# e. V → [+F] / CCCC# . . . I agree with Odden (1994) and others since the 1970’s that this infinity should be re-interpreted as locality. In recent years, this has been achieved representationally, (i.e., feature geometry and autosegmental tiers).

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 21 / 29

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Generalized Search & Copy

Adopting search allows us to maintain this basic result, but procedurally rather than representationally. Treating [+F] as a highly abstract affix allows the following: ς (initiator of search): [+F] γ (target of search): First V δ (direction of search): L β (beginning point of search): % Copy ς to γ No matter how many consonants come between % and the last vowel in the word, search will converge on the correct target.

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 22 / 29

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Generalized Search & Copy

Now, rather than copy adding a feature from the target (γ) to the initiator (ς), copy applies the other way around. Thus, copy must be made bidirectional:

Copy algorithm (bidirectional version)

Identify αF on γi and assign αF to ςi if the set of conditions C on γi are satisfied or Identify αF on ςi and assign αF to γi if the set of conditions C on γi are satisfied. I add a third primitive operation, delete, which interacts with search and copy to create the typology of feature-filling vs. feature-changing and pure spreading vs. spread-and-delink

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 23 / 29

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Generalized Search & Copy

I adopt the distinction between Path and F-element rules from Archangeli & Pulleyblank (1994): Parameter: Function Values: {Insert, Delete} Parameter: Type Values: {Path, F-element} Parameter: Direction Values: {Left-to-right, Right-to-left} Parameter: Iteration Values: {Iterative, Non-iterative}

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 24 / 29

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Generalized Search & Copy

Direction corresponds directly to the δ parameter on search. Type distinguishes spreading (Path) from insertion (F-type)

  • rules. For me, whether ς is in Σ or not.

Function corresponds roughly to my distinction between copy and delete operations, but deletion of a segment or string can also come from forward loops. Iteration is discussed in Samuels (2009), §4.4.4

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 25 / 29

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Conclusions

The primitive operations search, copy, & delete which I have introduced here, and which are explicated in greater detail in Chapter 4 of my thesis, work in concert to produce the range of attested phonological and morphophonological processes. The result is a procedural theory, similar in some respects to Autosegmental Phonology but with much slimmer representations. Future directions: experiments on the acquisition of phonological rules, particularly how children generalize and how anchors relate to other cognitive mechanisms, e.g., positional memory; comparisons between phonological and syntactic operations.

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 26 / 29

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SLIDE 45

Conclusions

The primitive operations search, copy, & delete which I have introduced here, and which are explicated in greater detail in Chapter 4 of my thesis, work in concert to produce the range of attested phonological and morphophonological processes. The result is a procedural theory, similar in some respects to Autosegmental Phonology but with much slimmer representations. Future directions: experiments on the acquisition of phonological rules, particularly how children generalize and how anchors relate to other cognitive mechanisms, e.g., positional memory; comparisons between phonological and syntactic operations.

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 26 / 29

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SLIDE 46

Conclusions

The primitive operations search, copy, & delete which I have introduced here, and which are explicated in greater detail in Chapter 4 of my thesis, work in concert to produce the range of attested phonological and morphophonological processes. The result is a procedural theory, similar in some respects to Autosegmental Phonology but with much slimmer representations. Future directions: experiments on the acquisition of phonological rules, particularly how children generalize and how anchors relate to other cognitive mechanisms, e.g., positional memory; comparisons between phonological and syntactic operations.

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 26 / 29

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SLIDE 47

Conclusions Thank you!

http://people.fas.harvard.edu/~bdsamuel

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 27 / 29

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SLIDE 48

References I

Archangeli, D., & D. Pulleyblank. 1994. Grounded phonology. Cambridge, MA: MIT Press. Chomsky, N., & M. Halle. 1968. The sound pattern of English. New York: Harper & Row. Dijkstra, E. W. 1959. A note on two problems in connexion with graphs. Numerische Mathematik 1:269–271. Fitzpatrick, J. M. 2006. Sources of multiple reduplication in Salish & beyond. MIT Working Papers on Endangered & Less Familiar Languages 7: Studies in Salishan:211–240. Gagnon, M. 2007. Token identity vs. type identity. Paper presented at the CUNY Phonology Forum Conference on Precedence Relations. Gagnon, M. 2008. On linearizing subtractive morphology. Ms., Concordia University. Gagnon, M., & M. Pich´

  • e. 2007. Principles of linearization & subtractive morphology. Paper

presented at the CUNY Phonology Forum Conference on Precedence Relations. Halle, M. 2008. Reduplication. In Foundational issues in linguistic theory: essays in honor

  • f Jean-Roger Vergnaud, ed. R. Freidin, C. Otero, & M.-L. Zubizarreta, 325–358.

Cambridge, MA: MIT Press. Hornstein, N. 2009. A theory of syntax: minimal operations & Universal Grammar. Cambridge: CUP. Hornstein, N., & P. Pietroski. To appear. Basic operations: minimal syntax-semantics. Catalan Journal of Linguistics .

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 28 / 29

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References II

Idsardi, W. J., & R. Shorey. 2007. Unwinding morphology. Paper presented at the CUNY Phonology Forum Workshop on Precedence Relations. Mailhot, F., & C. Reiss. 2007. Computing long-distance dependencies in vowel harmony. Biolinguistics 1:28–48. Marantz, A. 1982. Re reduplication. Linguistic Inquiry 13:435–482. Odden, D. 1994. Adjacency parameters in phonology. Language 70:289–330. Poeppel, D. 2005. The interdisciplinary study of language & its challenges. Jahrbuch des Wissenschaftkollegs zu Berlin . Raimy, E. 1999. Representing reduplication. Ph.D. dissertation, U. of Delaware. Raimy, E. 2000. Remarks on backcopying. Linguistic Inquiry 31:541–552. Samuels, B. 2009. The structure of phonological theory. Ph.D. dissertation, Harvard University. Yu, A. C. 2007. A natural history of infixation. Oxford: OUP. Zepeda, O. 1983. A Papago grammar. Tucson, AZ: U. of Arizona Press.

Bridget Samuels (Harvard) Primitive Operations in Phonology UMD - May 20, 2009 29 / 29